"Ah, swing, well, we used to call it ragtime, then blues–then jazz. Now, it's swing. White folks yo'all sho is a mess. Swing!" (Louis Armstrong's reply when asked to define swing music)
Big bands were prominent in the 1920's. However in stylistic terms they tended to play more popular "sweet" tunes than what is strictly known as jazz. They very much stuck to the melody as written and as such there was very little room for improvisation.
As an example here's the Paul Whiteman Orchestra, an extremely popular big band.
Jazz had reached something of a crossroads by 1929 - 1930. Louis Armstrong had lifted the bar significantly and all musicians that came after him had to live in his shadow. I would argue therefore that the music evolved in a positive direction - you really had to be good to cut it. There was also the rise of the radio - jazz could now be heard outside of the main cities and as such spread across the country sparking huge interest in Kansas City and all the way to Los Angeles.
However the main event that was to shape the music was indoubtedly the Wall Street Crash. In simplistic terms it saw the collapse of the U.S. economy which resulted in millions becoming unemployed. This of course included musicians and a number of notable examples were not to survive the crash, including Freddie Keppard, King Oliver and Jelly Roll Morton. A direct result saw the consolidation of musicians into bigger bands that was to have an sonic effect on the music. The big bands moved away from the sweet sound of the mid 20's towards a more authentic form of jazz. It is around this time that we see the emergence of figures like Benny Goodman and Count Basie.
Check out "Moten Swing" from Bernie Moten's Kansas City Orchestra featuring Count Basie. This recording was made in 1932 and perhaps demonstrates a good bridge between the 1920's and Swing Era of the 30's.